Yukawa textures from an extra {\bf U(1)} symmetry?

The observed hierarchy of the quark and lepton masses and mixing angles has led to the parametrisation of the mass matrices in powers of the Cabibbo angle and a certain number of zeros. The origin of these ``textures'' may lie in symmetries present at the GUT/string unification scale. We discuss the case of an extra $U(1)$. Symmetric textures with two or three zeros can be generated through high-order operators containing light/heavy Higgs multiplets and singlet fields. However, a realistic scenario for generating both the up- and down-quark mass matrices is not possible within the MSSM with an extra singlet. The presence of at least one pair of heavy Higgs multiplets and extra singlets are needed, and, even so, difficulties are encountered when extending this scenario to the neutrino sector through the mass relations of grand unification.